Lissajous dual-axial scan component and scan frequency generation method thereof

ABSTRACT

Disclosed herein are a Lissajous dual-axial scan component and a scan frequency generation method thereof. The Lissajous dual-axial scan component scans at a fast-axial resonant frequency and a slow-axial resonant frequency. A fast-axial bias frequency and a slow-axial bias frequency are determined according to the fast-axial resonant frequency and the slow-axial resonant frequency. Fast-axial positive integers and slow-axial positive integers are determined according to a system frequency, the fast-axial bias frequency, and the slow-axial bias frequency. An irreducible fraction is determined according to the fast-axial positive integers and the slow-axial positive integers as a ratio of the fast-axial bias frequency to the slow-axial bias frequency less than 10. A scan trace repetition frequency greater than 24 Hz is determined according to the irreducible fraction in order that the Lissajous dual-axial scan component scans according to the scan trace repetition frequency.

CROSS-REFERENCE TO RELATED APPLICATIONS

This non-provisional application claims priority under 35 U.S.C. §119(a) on Patent Application No. 201410131428.X filed in People's Republic of China on Apr. 2, 2014, the entire contents of which are hereby incorporated by reference.

TECHNICAL FIELD

The embodiments disclosed herein relate to a Lissajous dual-axial scan component and a scan frequency generation method thereof.

BACKGROUND

Micro-projection devices include pico-projectors and pocket projectors. The smaller, lighter pico-projectors are primarily integrated with mobile devices, e.g. cell phones, ultra-mobile PCs, and digital still cameras, and powered by the batteries of the mobile devices, but there are also independent pico-projectors. Pocket projectors are similar to traditional ones, only smaller and lighter.

Pico-projectors measuring only a few centimeters wide and a few micrometers thick have been developed to be embedded on cell phones. A pico-projector needs one dual-axial scan component or two single-axial scan components to project to a two-dimensional screen by laser scan. There are roughly two types of dual-axial scan projection: raster scan and Lissajous scan. The two axes are generally a fast axis and a slow axis. The slow axis of a raster scan must be kept at 60 Hz and the fast axis is usually above 18 kHz to attain high-quality, high-resolution, and non-flickering projected screens. It is impossible for the resonant frequency of a scan component to be as low as 60 Hz; hence the component is forced-actuated quasi-statically to vibrate at that frequency.

${\theta = \frac{T}{K}},$

The quasi-static force is related to the scanning angle by where T is the torque caused by the driving force, K is the stiffness of the twisting axis, and θ is the scanning angle. The greater the force, the larger the angle. The scanning angle can also be increased by lowering K and sacrificing the strength of the component, where the twisting axis is easily broken. A large K, however, implies increased driving force and power consumption, despite strengthening the component.

The slow axis of a Lissajous scan is not limited to 60 Hz, but configurable according to the scan structure. When the actuator drives at the resonant frequency, the scanning angle is expressed as

${\theta = {Q\frac{T}{K}}},$

where Q is the quality factor of the component. Q is greater than 1500 for a common scan component made of silicon. Resonance, therefore, significantly magnifies vibrational displacement, achieving large-angle scanning even with a smaller force and lower power consumption (50 mW for instance). Consequently a Lissajous scan component can be configured to different resonant frequencies according to need and is thus more flexible in structural design.

In short, a raster scan component consumes more power but generates projections with parallel lines, less flicker, and higher scan line coverage. A Lissajous scan component, driven vertically and horizontally at resonant frequencies, consumes less power, but is less predictable with its complex scan trace, which calls for additional analysis and research. Moreover, whether a Lissajous scan screen flickers is a question of the scan line density and the frequency ratio.

SUMMARY

The present disclosure provides a scan frequency generation method of a Lissajous dual-axial scan component. The Lissajous dual-axial scan component scans at a fast-axial resonant frequency and a slow-axial resonant frequency. A fast-axial bias frequency and a slow-axial bias frequency are determined according to the fast-axial resonant frequency and the slow-axial resonant frequency. A plurality of fast-axial positive integers and a plurality of slow-axial positive integers are determined according to a system frequency, the fast-axial bias frequency, and the slow-axial bias frequency. An irreducible fraction is determined according to the fast-axial positive integers and the slow-axial positive integers. The irreducible fraction is a ratio of the fast-axial bias frequency to the slow-axial bias frequency, the ratio being less than 10. A scan trace repetition frequency is determined according to the irreducible fraction in order that the Lissajous dual-axial scan component scans according to the scan trace repetition frequency, which is greater than 24 Hz.

The present disclosure also provides a Lissajous dual-axial scan component comprising a frame, a mass, a mirror, a pair of fast axes, and a pair of slow axes. When the Lissajous dual-axial scan component is driven, the fast axes are configured to twist at a fast-axial resonant frequency and the slow axes are configured to twist at a slow-axial resonant frequency. The mass is connected to the frame through the pair of slow axes. The mirror is connected to the mass through the pair of fast axes. The Lissajous dual-axial scan component, when driven, scans according to a scan trace repetition frequency and a ratio of a fast-axial bias frequency to a slow-axial bias frequency. The scan trace repetition frequency is greater than 24 Hz. The ratio is less than 10. The fast-axial bias frequency and the slow-axial bias frequency are determined according to the fast-axial resonant frequency and the slow-axial resonant frequency.

BRIEF DESCRIPTION OF THE DRAWING

The present disclosure will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only and thus are not limitative of the present disclosure and wherein:

FIG. 1 illustrates a Lissajous dual-axial scan component, in accordance with an embodiment disclosed.

FIG. 2 illustrates is a scan frequency generation method of a Lissajous dual-axial scan component, in accordance with an embodiment disclosed.

FIG. 3 illustrates a Lissajous scan trace, in accordance with an embodiment disclosed.

FIGS. 4A to 4D illustrate scan traces under different values of m and n.

FIG. 5A is an enlargement in part of the scan trace of FIG. 4B.

FIG. 5B is an enlargement in part of the scan trace of FIG. 4D.

FIG. 6 illustrates the effect of slow-axial resonant frequency on scan line density.

DETAILED DESCRIPTION

The embodiments hereby disclosed of a Lissajous dual-axial scan component and a scan frequency generation method attend to both coverage and flicker issues of Lissajous scan projections, enhancing scan line density and resolution.

In the following detailed description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the disclosed embodiments. It will be apparent, however, that one or more embodiments may be practiced without these specific details. In other instances, well-known structures and devices are schematically shown in order to simplify the drawings.

A Lissajous dual-axial scan component (hereafter referred to as the component) is depicted in FIG. 1. Please note that the shape, size, and dimensions of the component in the figure are for illustration only and not limitative of the shape, size, and dimensions of an actual component. The component comprises fast axes 11 and 12, slow axes 15 and 16, a mirror 13, a mass 14, and a frame 17. The mirror 13 is disposed at the center and connected to the mass 14 through the pair of fast axes 11 and 12. The mass 14 is connected to the frame 17 through the pair of slow axes 15 and 16. Laser light shines upon the mirror 13 and is reflected to a screen. When the component is driven by an actuator, the fast axes 11 and 12 twist at a fast-axial resonant frequency, causing the mirror 13 to perform fast-axial scan, and the slow axes 15 and 16 twist at a slow-axial resonant frequency, causing the mirror 13 to perform slow-axial scan. The fast axes 11 and 12 are perpendicular to the slow axes 15 and 16, thus bringing forth scan projections.

The component, when driven, scans according to a scan trace repetition frequency greater than 24 Hz and a ratio of a fast-axial bias frequency to a slow-axial bias frequency, the ratio being less than 10. The fast-axial bias frequency and the slow-axial bias frequency are determined according to the fast-axial resonant frequency and the slow-axial resonant frequency.

In one embodiment, the component may be piezoelectrically, electrostatically, or electromagnetically driven. In one embodiment, the component is made of piezoelectric material.

A scan frequency generation method of the component is depicted in FIG. 2. The component has two resonant frequencies f_(x0) and f_(y0). The component magnifies the scanning angles by resonance. The scanning angles are at their maxima when the driving frequencies are f_(x)=f_(x0) and f_(y)=f_(y0).

In practice, the driving frequencies may deviate from the resonant frequencies. Despite slight decrease in the scanning angles, the driving frequencies can be more flexibly chosen thus, relatively speaking. Therefore, the fast- and slow-axial bias frequencies can be chosen according to the resonant frequencies associated with maximum scanning angles.

To begin with, the fast-axial bias (driving) frequency f_(x) and the slow-axial bias (driving) frequency f_(y) are determined S20 according to the fast-axial resonant frequency f_(x0) and the slow-axial resonant frequency f_(y0). A plurality of fast-axial positive integer M's and a plurality of slow-axial positive integer N's are then determined S21 according to f_(x), f_(y), and a system frequency f_(clk). In one embodiment, the fast- and slow-axial frequencies are found according to

$f_{x} = {{\frac{f_{clk}}{N}\mspace{14mu} {and}\mspace{14mu} f_{y}} = {\frac{f_{clk}}{M}.}}$

All possible M's and N's are thereby obtained. Assume that there are i fast-axial positive integers M₁, M₂, . . . , and j slow-axial positive integers N₁, N₂, . . . , N_(j), then there are i·j frequency combinations. Two positive integers M and N are chosen so that f_(x)=a·M and f_(y)=a·N, where a is an arbitrary number. As a result,

$\frac{f_{x}}{f_{y}} = {\frac{M}{N}.}$

The resonant frequencies are related to the bias frequencies by

|f _(x) −f _(x0) |≦Δf _(x)

|f _(y) −f _(y0) |≦Δf _(y)

where Δf_(x) is the fast-axial frequency bias and Δf_(y) is the slow-axial frequency bias. Consequently,

${{\frac{f_{clk}}{N} - f_{x\; 0}}} \leq {\Delta \; f_{x}}$ ${{\frac{f_{clk}}{M} - f_{y\; 0}}} \leq {\Delta \; f_{y}}$

In other words,

$\frac{f_{clk}}{f_{x\; 0} - {\Delta \; f_{x}}} \geq N \geq \frac{f_{clk}}{f_{x\; 0} + {\Delta \; f_{x}}}$ $\frac{f_{clk}}{f_{y\; 0} - {\Delta \; f_{y}}} \geq M \geq \frac{f_{clk}}{f_{y\; 0} + {\Delta \; f_{y}}}$

The M's and N's can be obtained according to the above inequalities.

An irreducible fraction, as a ratio of a fast-axial frequency to a slow-axial one, or f_(x) to f_(y), is determined S22 according to the M's and N's. The ratio is less than 10. Each of the found frequency combinations corresponds to an irreducible fraction m/n. A scan trace repetition frequency f_(rep) is determined S23 according to the irreducible fraction m/n and the equation

$f_{rep} = {\frac{f_{x}}{m} = {\frac{f_{y}}{n} \cdot f_{rep}}}$

needs to be greater than 24 Hz. Lowering m/n by increasing the slow-axial frequency provides a balance between high coverage of and less flicker on the screen. Finally, the component scans S24 according to f_(rep).

The scan frequency generation method described above is hereby elaborated upon, especially regarding the determination of the ratio as less than 10 and f_(rep) as greater than 24 Hz.

A Lissajous scan takes time t as a parameter. The scan trace are defined as

x(t)=A sin(2π·f _(x) ·t)

y(t)=B sin(2π·f _(y) ·t+φ)

where A and B are constants, f_(x) is a fast-axial frequency, f_(y) is a slow-axial frequency, and φ is a phase difference. According to the above definition, the scan trace forms a projected screen of area 2A·2B=4AB.

In one embodiment, the frequencies are generated with a divider; that is, f_(x) and f_(y) are derived from a system frequency f_(clk) with the use of a counter. Specifically, the counter generates the integers M and N, and

$a = \frac{f_{clk}}{M \cdot N}$

is taken. It follows that

$f_{x} = {{\frac{f_{clk}}{N}\mspace{14mu} {and}\mspace{14mu} f_{y}} = {\frac{f_{clk}}{M}.}}$

The aforesaid ratio is then

${r = {\frac{f_{x}}{f_{y}} = {\frac{M}{N} = \frac{m}{n}}}},$

where m/n is the irreducible fraction, m and n are coprime, and r is rational. Please note that as long as r is rational, it does not matter how the frequencies are generated, the divider being only an example.

In another embodiment, the frequencies are determined with a direct digital synthesizer (DDS). Specifically, the counter decides the integers M and N, and

$a = \frac{f_{clk}}{2^{q}}$

is taken, where q is an arbitrary positive integer. It follows that

$f_{x} = {{\frac{f_{clk}M}{2^{q}}\mspace{14mu} {and}\mspace{14mu} f_{y}} = {\frac{f_{clk}N}{2^{q}}.}}$

In yet another embodiment, the frequencies are determined with a phase lock loop (PLL). Specifically, the counter decides the integers M, N, and p, and

$a = \frac{f_{clk}}{p}$

is taken. It follows that

$f_{x} = {\frac{f_{clk}M}{p}\mspace{14mu} {and}\mspace{14mu} {\frac{f_{clk}N}{p}.}}$

Substituting the above expressions of f_(x) and f_(y) into the aforesaid inequalities yields various ranges of M and N.

The scan position at t=t₀ is

$\quad\left\{ \begin{matrix} {{x\left( t_{0} \right)} = {A\; {\sin \left( {2{\pi \cdot f_{x} \cdot t_{0}}} \right)}}} \\ {{y\left( t_{0} \right)} = {B\; {\sin \left( {{2{\pi \cdot f_{y} \cdot t_{0}}} + \varphi} \right)}}} \end{matrix} \right.$

Since r is rational, the scan trace repeats itself within a limited amount of time.

Consider the case where at t=r the scan trace returns to how it was at t=t₀; that is,

$\quad\left\{ \begin{matrix} {{\sin \left( {2{\pi \cdot f_{x} \cdot t_{0}}} \right)} = {\sin \left( {2{\pi \cdot f_{x} \cdot \tau}} \right)}} \\ {{\sin \left( {{2{\pi \cdot f_{y} \cdot t_{0}}} + \varphi} \right)} = {\sin \left( {{2{\pi \cdot f_{y} \cdot \tau}} + \varphi} \right)}} \end{matrix} \right.$

Also

$f_{rep} = {\frac{1}{\tau - t_{0}}.}$

By periodicity of trigonometric functions,

$\quad\left\{ \begin{matrix} {{{2{\pi \cdot f_{x} \cdot t_{0}}} + {2{\alpha\pi}}} = {2{\pi \cdot f_{x} \cdot \tau}}} \\ {{{2{\pi \cdot f_{y} \cdot t_{0}}} + {2{\beta\pi}}} = {2{\pi \cdot f_{y} \cdot \tau}}} \end{matrix} \right.$

where α and β are positive integers. Simplifying the above gives

$\quad\left\{ \begin{matrix} {\alpha = {f_{x}\left( {\tau - t_{0}} \right)}} \\ {\beta = {f_{y}\left( {\tau - t_{0}} \right)}} \end{matrix} \right.$

In other words,

$\frac{f_{x}}{f_{y}} = {\frac{\alpha}{\beta}.}$

The irreducible fraction of

$\frac{f_{x}}{f_{y}}$

is m/n; therefore, α=m and β=n can be taken. Given that

${f_{rep} = \frac{1}{\tau - t_{0}}},$

it follows that

$f_{rep} = {\frac{f_{x}}{m} = {\frac{f_{y}}{n}.}}$

f_(rep) needs to be greater than 24 Hz for the projected screen not to flicker, considering the persistence of human vision.

A Lissajous scan trace is depicted on the x-y plane in FIG. 3. The squares represent where the scan trace intersects with x=A; the triangles represent where the scan trace intersects with y=B. The number of the squares is defined as m, and that of the triangles as n. The closer a pattern formed by intersecting scan lines is to the center of the screen, the more it resembles a rhombus. The quasi-rhombus at the center of the screen (the shaded area in the figure) has diagonals of lengths

${L_{1} \approx {\frac{A\; \pi}{n}\mspace{14mu} {and}\mspace{14mu} L_{2}} \approx \frac{B\; \pi}{m}};$

therefore,

${\frac{L_{1}}{L_{2}} \approx \frac{Am}{Bn}},$

and the larger is r, the flatter is the quasi-rhombus.

The size of the shaded area in FIG. 3 may serve as an indicator of the scan coverage. L in the figure, for example, can be expressed as

$L \approx {\sqrt{\left( \frac{L_{1}}{2} \right)^{2} + \left( \frac{L_{2}}{2} \right)^{2}}\mspace{14mu} {or}\mspace{14mu} L} \approx {\frac{\pi}{2}{\sqrt{\left( \frac{A}{n} \right)^{2} + \left( \frac{B}{m} \right)^{2}}.}}$

It is evident from the above expression that the larger m and n are, the smaller is L, and the higher the scan coverage. Moreover, from

${f_{rep} = {\frac{f_{x}}{m} = \frac{f_{y}}{n}}},$

given a f_(rep), the larger m and n are, the higher f_(x) and f_(y) need to be. The fast-axial f_(x) of a common MEMS scan component for projection is typically about 15 kHz or above. With f_(x)=20 kHz, for example, the largest m is about 833 when f_(rep) is required to be 24 Hz or above.

FIGS. 4A to 4D illustrate scan traces under m=651 and different values of n. The frequency ratio r and L₁/L₂ are both larger in FIGS. 4A and 4B, where n is 22 and 44, respectively, rendering m/n greater than 10. There are clearly discernible dense and sparse portions on the projected screen of FIG. 4A. They can be observed in FIG. 4B, too, though they are less conspicuous in FIG. 4B than in FIG. 4A, due to a decreased r. The dense-sparse contrast is not immediately obvious in FIG. 4C, where n=68 and m/n is less than 10, and is much improved in FIG. 4D, where n=226 and m/n is less than 5. Per the foregoing description, for a fast-axial resonant frequency greater than 15 kHz, the slow-axial frequency has to be greater than 1.5 kHz given that m/n is 10, or greater than 3 kHz when m/n is less than or equal to 5.

As an enlargement in part of FIG. 4B, FIG. 5A shows a projected screen with clear dense and sparse portions due to the flat rhombi. FIG. 5B, on the other hand, is an enlargement in part of FIG. 4D, where the aspect ratio of the rhombi is lower, rendering the dense-sparse contrast almost non-existent.

FIG. 6 illustrates a feature of the present disclosure, i.e. increasing the slow-axial frequency. The effect on L* of increasing the slow-axial frequency is evident from the figure. Here L* is a dimensionless expression of L; that is,

$L^{*} \approx {\frac{\pi}{2}\sqrt{\left( \frac{1}{n} \right)^{2} + \left( \frac{1}{m} \right)^{2}}}$

with A=B=1. When the fast-axial f_(x0)=24.5 kHz and Δf_(x)=Δf_(y)=5 Hz, the larger the slow-axial f_(y0) (from 1, 2, 5, 10, 15, to 20 kHz for instance), the larger 1/L* is and the smaller L* is for certain f_(x) and f_(y) pairings, giving rise to higher scan coverage.

A scan component of laser projection must operate at two frequencies, fast and slow, to from a Lissajous scan. The present disclosure provides a type of Lissajous scan frequency combination, attending to both coverage and flicker issues of Lissajous scan projections.

The slow axis is underutilized in prior art. Most prior art relates to mechanisms operating under high frequency ratios, which translate to low-frequency slow axes. In contrast, the slow-axial frequency is increased in the present disclosure to enhance the resolution of projected screens.

In addition, there is a trade-off between refresh rate and scan line density. When the ratio of the fast-axial frequency to the slow-axial frequency is greater than 10, the scan line density is low. According to the present disclosure, the scan line density is apparently increased when the ratio is less than 10, and especially so when it is less than 5.

Heightening the slow-axial frequency by lowering the ratio under the same refresh rate increases the scan line density 1/L* and the screen resolution. The screen is even more stable and flickers less when the refresh rate is increased. With the present disclosure, it is possible for Lissajous scans to achieve excellent projection quality without losing its merits like low driving power. Performance and cost, therefore, are reconciled.

The foregoing description has been presented for purposes of illustration. It is not exhaustive and does not limit the disclosure to the precise forms or embodiments disclosed. Modifications and adaptations will be apparent to those skilled in the art from consideration of the specification and practice of the disclosed embodiments. It is intended, therefore, that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims and their full scope of equivalents. 

What is claimed is:
 1. A scan frequency generation method of a Lissajous dual-axial scan component, the Lissajous dual-axial scan component configured to scan at a fast-axial resonant frequency and a slow-axial resonant frequency, the scan frequency generation method comprising: determining a fast-axial bias frequency and a slow-axial bias frequency according to the fast-axial resonant frequency and the slow-axial resonant frequency; determining a plurality of fast-axial positive integers and a plurality of slow-axial positive integers according to a system frequency, the fast-axial bias frequency, and the slow-axial bias frequency; determining an irreducible fraction according to the fast-axial positive integers and the slow-axial positive integers, the irreducible fraction being a ratio of the fast-axial bias frequency to the slow-axial bias frequency, the ratio being less than 10; determining a scan trace repetition frequency according to the irreducible fraction; and scanning by the Lissajous dual-axial scan component according to the scan trace repetition frequency, the scan trace repetition frequency being greater than 24 Hz.
 2. The scan frequency generation method of claim 1, wherein the fast-axial resonant frequency or the slow-axial resonant frequency is a resonant frequency associated with a maximum scanning angle.
 3. The scan frequency generation method of claim 1, wherein the fast-axial resonant frequency is greater than 15 kHz.
 4. The scan frequency generation method of claim 3, wherein the slow-axial resonant frequency is greater than 1.5 kHz.
 5. The scan frequency generation method of claim 1, wherein the ratio is less than
 5. 6. The scan frequency generation method of claim 5, wherein the fast-axial resonant frequency is greater than 15 kHz.
 7. The scan frequency generation method of claim 6, wherein the slow-axial resonant frequency is greater than 3 kHz.
 8. A Lissajous dual-axial scan component comprising: a frame; a pair of fast axes configured to twist at a fast-axial resonant frequency when the Lissajous dual-axial scan component is driven; a pair of slow axes configured to twist at a slow-axial resonant frequency when the Lissajous dual-axial scan component is driven; a mass connected to the frame through the pair of slow axes; and a mirror connected to the mass through the pair of fast axes; wherein the Lissajous dual-axial scan component, when driven, scans according to a scan trace repetition frequency and a ratio of a fast-axial bias frequency to a slow-axial bias frequency, the scan trace repetition frequency being greater than 24 Hz, the ratio being less than 10; wherein the fast-axial bias frequency and the slow-axial bias frequency are determined according to the fast-axial resonant frequency and the slow-axial resonant frequency.
 9. The Lissajous dual-axial scan component of claim 8, wherein the fast-axial resonant frequency or the slow-axial resonant frequency is a resonant frequency associated with a maximum scanning angle.
 10. The Lissajous dual-axial scan component of claim 8, wherein the Lissajous dual-axial scan component is piezoelectrically driven.
 11. The Lissajous dual-axial scan component of claim 8, wherein the Lissajous dual-axial scan component is electrostatically driven.
 12. The Lissajous dual-axial scan component of claim 8, wherein the Lissajous dual-axial scan component is electromagnetically driven.
 13. The Lissajous dual-axial scan component of claim 8, wherein the fast-axial resonant frequency is greater than 15 kHz.
 14. The Lissajous dual-axial scan component of claim 13, wherein the slow-axial resonant frequency is greater than 1.5 kHz.
 15. The Lissajous dual-axial scan component of claim 8, wherein the ratio is less than
 5. 16. The Lissajous dual-axial scan component of claim 15, wherein the fast-axial resonant frequency is greater than 15 kHz.
 17. The Lissajous dual-axial scan component of claim 16, wherein the slow-axial resonant frequency is greater than 3 kHz. 